Here we look at captains with no wins, no losses and no draws.
No Wins:

These are captains in 4 or more Tests with no wins.
Headed by M Ashraful of Bangladesh with 13 (12 losses and 1 draw). The next (IT Botham) is more surprising. Another Bangladeshi Khaled Mashud also has 12.
In recent years there are AG Cremer (8) and KC Brathwaite (5).
From India there are MH Mankad (6), S Venkataraghavan (5) and others with 4.
No losses:

These are captains in 2 or more Tests with no losses.
WW Armstrong with 10 heads this list, with 8 wins and 2 draws.
Next are DB Close and FG Mann with 7.
In recent years there is only AM Rahane with 2; both of these wins were when he was standing in for Kohli.
From India we also have Srikkanth with 4 (all draws).
No draws:

These are captains in 3 or more Tests with no draws.
Headed by Waqar Younis (17, 10 wins and 7 losses). The next is Shakib with 14 (3 wins and 11 losses).
Others from recent times (other than Shakib) include R Herath, KC Brathwaite and RAS Lakmal with 5.
Brathwaite has 5 losses out of 5.
From India there is DK Gaekwad with 4 (all losses). He is presently India’s oldest living Test player.